**1. Introduction**

The study of stratification analyzes the variations and effects in thermal stratified object (medium) for the so-called common fluids. In industrial as well as natural processes, stratification plays an important role. Reason behind the existence of this phenomena is variation in temperature, variation of densities in different fluids and the concentration differences. Transfer of heat and mass simultaneously, doubles the stratification that belongs to the context of thermal stratification. Thermal stratification can be seen very often in the reservoirs and oceans. Another type of stratification is salinity stratification that is witnessed in rivers, estuaries, reservoirs storing the ground water, atmospheric heterogeneous mixtures, food industries and various manufacturing processes etc. A very few researchers in the past have made a significant contribution in investigating the effect of mass and thermal stratification over heat as well as mass transfer by a naturally convective flow. Keeping in view the above mentioned facts, double stratification gained a significant importance in the eyes of some researchers like Srinivasacharya and RamReddy [1,2] who investigated the double stratification's effect numerically. The medium was first considered non-porous and afterwards Darcian (porous) as well. Mixing process of oxygen with water in the bottom of reservoirs through biological processes can be controlled by using the tool of thermal stratification (see [3]). Stratification has also major contribution in environmental sciences. It can be very helpful in balancing the temperature differences and concentrations of oxygen and hydrogen to control the growth rates of various species in naturally unbalanced and less productive environments, Ibrahim and Makinde [4]. Various engineering processes occurring at a very high temperature direly depend upon a deep understanding and knowledge of thermal radiation. Combustion energy processes happening in fossil fuel, flows in astrophysics, harnessing the energy of sun in solar technology, turbines, devices for converting mechanical energy into propulsive force in aircraft, missiles and space-ships etc. are best examples of the importance and usage of the study of thermal radiations (see [5]). In some objects, fluid flow encounters a certain point where fluid motion becomes zero. In Geop physical setups, physical models and fluid mechanics, the point is called stagnation point. This stagnation point can be anywhere on the surface of object. However, the fluid continues flowing in neighborhood of this point, called stagnation point flow. Such an object is termed as impermeable object (see [6]). Stagnation point is sub-divided into two main categories (i) orthogonal and (ii) slanted stagnation point. In first case, the fluid particles act orthogonal to a rigid/solid surface and consequently, the resulting velocity is zero. The orthogonality of fluid particles at certain point makes it a perpendicular or orthogonal stagnation point. In second case, the fluid particles act on the rigid body through some random arbitrary angle of incidence. One can say that this point is a dual of orthogonal and shear stagnation point flow flowing parallel to the object. Numerous researches has been carried out on stagnation point flow. Describing the fluid motion near stagnation regions of a solid surface, the stagnation point flow was first studied by Hiemenz [7] using a similarity transformation for reducing the Navier-Stokes equations to Non-linear ODEs. Accordingly, stagnation flow can be categorized in various types depending upon the behavior of flow. Analyzing the density one can characterize it as inviscid or viscous flow, steady or unsteady flow, geometrically it can be two or three dimensional flow. The stagnation point flow can also be characterized according to the symmetry. Therefore, it can be symmetric or asymmetric, normal or slanted. Analyzing the flow behavior, it can be treated as homogeneous or immiscible fluid and forward or reverse fluid (see [8,9]). Importance of stagnation point flow can be witnessed in natural and industrial phenomena. Fluid striking the tips of submarines, oil-ships and air-crafts are best examples of stagnation point flow. The blood flowing through a junction in an artery is another biological example of stagnation point flow. Mabood et al. [10] investigated the radiation effects on stagnation point flow with melting heat transfer. Meanwhile, stagnation point flow of Tangent-hyperbolic liquid visualized by Shafiq et al. [11] witnesses its importance and significance in different aspects.

Process of natural convection can be witnessed in various physical phenomenon especially fire and heat engineering, nuclear science, reservoirs used for petroleum etc. The presence of heat (source/sink) and thermal radiation is a key factor in natural convection process. Such processes has been studied extensively because of naturally frequent existence. Ghoshdastidar [12] has explained various areas witnessing the applications of free convection. For example, the transfer of heat from heater to the neighborhood or heat dissipation through coil of refrigerator unit to the neighborhood etc. The encounter of such phenomena is common in wide range of thermal applications. Cheng [13,14] studied the boundary layer flow as natural convection. The medium was a vertical surface with Newtonian heating. The chemical reaction and thermal radiation are important aspects in engineering setups involving Riga patterns (see [15]). Boundary layer flow and the study of heat transfer in fluid mechanics and engineering is a contemporary research area (see [16]). Furthermore, Rasool et al. [17] reported MHD nanofluid flow over stretching surface with simple temperature attributes whereas, Rasool et al. [18] reported a study in the same representation using Cattaneo Christov heat and mass flux model over a stretching surface. Many researchers in the past have remained focused on this area and their work have been published. For example Kuznetsov and Nield [19] studied this phenomena of boundary layer flow analytically using the Brownian motion model. The effects of thermophoresis were taken into account. The results proved that Nusselt number is a decreasing function of the parameters of Brownian motion. Presence of gravity is a key element for density differences which plays a vital role in the mixing of heterogeneous fluids and their dynamics. A similar kind of boundary layer flow through a porous medium was investigated by Lesnic et al. [20]. Recently, Shafiq et al. [21]

investigated a boundary-Layer flow of Walters' B fluid in Newtonian heating depicted the heat transfer phenomena. The study highlights usefulness of boundary layer flow. The Newtonian heating, its effects and applications has been discussed in this research in detail. The study of two-dimensional boundary layer flow using an unsteady and permeable stretching surface is ye<sup>t</sup> another recent improvement linking the effects of thermal radiations in boundary layer flows (see [22]). In this study Shafiq et al. investigated the effects of electric and magnetic fields. In present study the analysis is carried out by finding the optimal convergence. For details one can read the optimal control convergence procedure adopted in solving linearized Navier-Stokes equations in netlike domain [23] and pipeline flow [24].

In the literature mentioned above, the studies have been mainly reported on stretching surfaces with various assumptions including the porosity factor, Brownian diffusion and thermophoresis using HAM [25–31]. However, no research is found emphasizing the role of stagnation point in third grade fluid towards stretching surface (cylinder) which affirms the novelty of the present problem. Here the objective is to discuss the stagnation point and boundary layer flow, to analyze the corresponding results in the presence of sink/source and to graphically interpret various physical parameters involved in model using Optimal Homotopy approach.
